The Swendsen-Wang process does not always mix rapidly

Vivek K. Gore, Mark R. Jerrum
1997 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing - STOC '97  
The Swendsen-Wang process provides one possible dynamics for the Qstate Potts model in statistical physics. Computer simulations of this process are widely used to estimate the expectations of various observables (random variables) of a Potts system in the equilibrium (or Gibbs) distribution. The legitimacy of such simulations depends on the rate of convergence of the process to equilibrium, often known as the mixing rate. Empirical observations suggest that the Swendsen-Wang process mixes
more » ... ly in many instances of practical interest. In spite of this, we show that there are occasions on which the Swendsen-Wang process requires exponential time (in the size of the system) to approach equilibrium.
doi:10.1145/258533.258662 dblp:conf/stoc/GoreJ97 fatcat:uwxk3c5gnrcnnaghavra5jav3q